We show that the strong slope conjecture implies that the degree of the colored Jones polynomial detects all torus knots. As an application we obtain that an adequate knot that has the same colored Jones polynomial degrees as a torus knot must be a $(2,q)$-torus knot.
The author was supported in part by NSF grant DMS-1708249.
"The strong slope conjecture and torus knots." J. Math. Soc. Japan 72 (1) 73 - 79, January, 2020. https://doi.org/10.2969/jmsj/81068106